A049881 a(n) is the number of distinct sums of 3 different primes chosen from the first n primes.

1, 4, 10, 16, 23, 30, 38, 47, 57, 67, 77, 87, 96, 106, 116, 129, 140, 151, 160, 172, 183, 194, 208, 220, 231, 242, 252, 261, 279, 292, 304, 319, 334, 346, 360, 374, 389, 400, 413, 426, 440, 452, 464, 476, 488, 505, 524, 538, 552, 563, 576, 591, 604, 615, 625, 645, 659, 673, 683, 698, 716, 733

Offset

3,2

Links

Table of n, a(n) for n=3..64.

Example

From Petros Hadjicostas, Nov 19 2019: (Start)
The first 3 primes are 2, 3, and 5, and they form only one sum, so a(4) = 1.
The first 4 primes are 2, 3, 5, and 7, and they form 4 distinct sums each with three different terms (10, 12, 14, 15), so a(2) = 4.
The first 5 primes are 2, 3, 5, 7, and 11, and they form 13 distinct sums each with three different terms (10, 12, 14, 15, 16, 18, 19, 20, 21, 23), so a(5) = 10.
(End)

Maple

f := proc(n) local v, i, j, k;  v := {};
      if 3 <= n then
         for i from 1 to n - 2 do
         for j from i + 1 to n - 1 do
         for k from j + 1 to n do
         v := v union {ithprime(i) + ithprime(j) + ithprime(k)};
         end do; end do; end do;
      end if; nops(v); end proc;
seq(f(n), n=3..40); #

Prog

(PARI) a(n)={my(pr=primes(n), sums=Set()); for(i=1, n-2, for(j=i+1, n-1, for(k=j+1, n, s=pr[i]+pr[j]+pr[k]; sums=setunion(sums, Set(s)))); ); length(sums); }
for(n=3, 40, print1(a(n)", ")) \\ Petros Hadjicostas, Nov 19 2019 by modifying Michel Marcus's PARI program in A049880

Crossrefs

Cf. A000040, A049880, A049882, A253250.

Sequence in context: A341983 A184527 A246297 * A341064 A366661 A271911

Adjacent sequences: A049878 A049879 A049880 * A049882 A049883 A049884

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 19 2019

Status

approved